A certain problem is quantum mechanics has been shown to be uncomputable. This means that although it is in a certain sense making a prediction, there is no systematic way to determine what prediction this is, in the same way given a program, there is no systematic way to determine if it halts.
No, this does not mean that quantum mechanics will screech to a halt. No, this does mean that quantum mechanics will be discarded as metaphysics. I do feel though that this will affect the philosophy of mechanics, and science as a whole.
As for an analogy, Godel's Incompleteness Theorem had vast effects on the philosophy of mathematics. It did not wreck mathematics, but its philosophy, and even some parts of mathematics itself, where changed. The Halting Problem, which is related to this Theorem, has had closely related effects.
My question is, what effect does undecidable problems in Quantum Mechanics on the philosophy of science. What are the philosophical implications. In particular, part of the philosophy of science is that theories must be able to generate predictions. Although there technically is a prediction in this case, it is not effectively decidable in general.
Is it really making a prediction, if there is literally no way to find it? Is it falsifiable if there is no procedure with which to falsify it?